Rutile or C4 Crystal Structure

(TiO2 prototype) •Not all structures have to be cubic or hexagonal lattices in order to be close packed. •Rutile is an example of a non-cubic close packed structure. It’s tetragonal close packed •How many formula units? O Ti p. 680(585) in DeGraef

HCP array of O2- anions

•Since the ratio of Ti4+ to O2- is 1:2 and there is one octahedral site per O2- ion, only one-half of the octahedral (O) sites will be occupied by Ti Analogous to: (filling every other row along [100]). •Filled rows are staggered in every other layer. •Other compounds with •Octahedra are linked in rutile structure: CrO2, bands by sharing horizontal GeO , MoO , TaO , WO , edges. 2 2 2 2 •Octahedra of neighboring [010] 1 MgF2, ZnF2, NiF2, etc. chains share corners. Rutile (TiO2) Structure (continued)

Ti:CN=6 based on r; thus O:CN=3 •Octahedra of neighboring chains share corners.

•Octahedra are linked in bands by sharing horizontal edges.

[100] Projection down the [010]:

•The Ti ions occupy half of the OH sites by filling every other row along [100]. •The filled rows are staggered in every 2 other layer. Perovskite or E21 Crystal Structure (BaTiO3 prototype) •Example that cations and anions can mix on eutactic sites.

•For BaTiO3, an important ferroelectric, it’s a combination of Ba and O that form the cubic close packed framework. (O ions occupy ¾ of the CCP sites and the Ba ions occupy the remaining ¼ ). •How many formula units?

•Ti: 6 coordinated to oxygen (octahedron): TiO6 octahedron •Ba: 12 coordinated to oxygen (ccp): BaO12 cuboctahedron •O: 4 coordinated to Ba and 2 coordinated to Ti (→ at any O site, 2 octahedra and 4 cuboctahedra are shared) TiO6 octahedron p. 672/578 in DeGraef Share corners 2 x 2 x 2 unit cells

BaO12 cuboctahedron

Share square faces 3 Cuboctahedron (CN=12)

A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each, and 24 identical edges, each separating a triangle from a square.

8 triangular/6 square faces

Another example: Ca1-xYxF2+x (0 < x < 0.32): mineral Tveitite (x=0.25-0.27), which contains an ordered calcium yttrium-fluoride phase with excess fluoride ions located in cuboctahedron clusters. 4 Alternate Representation of Perovskite Structure •Instead of Ti at the center, the Ti can also be at cell vertices and the Ba in the center site. •Oxygen is now on midpoint of cell edges. •Still maintain 1 formula unit/unit cell •Nothing changes in terms of CN:

•Ti: 6 coordinated to oxygen (octahedron): 8 corner sharing TiO6 octahedrons at cell vertices. •Ba: 12 coordinated to oxygen (ccp): BaO12 cuboctahedron in center (central cavity) of unit cell formed by the 8 connected TiO6 octahedra. •O: 4 coordinated to Ba and 2 coordinated to Ti O2− Ti4+

Ba2+

5 Experimental Evidence of Perovskite Structure

[110]

[110]

[110]

Sr2+ 6